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https://hdl.handle.net/10316/8984
Title: | Supraconvergence and Supercloseness of a Scheme for Elliptic Equations on Nonuniform Grids | Authors: | Ferreira, J. A. Grigorieff, R. D. |
Issue Date: | 2006 | Citation: | Numerical Functional Analysis and Optimization - Taylor & Francis. 27:5 (2006) 539-564 | Abstract: | In this paper, we study the convergence of a finite difference scheme on nonuniform grids for the solution of second-order elliptic equations with mixed derivatives and variable coefficients in polygonal domains subjected to Dirichlet boundary conditions. We show that the scheme is equivalent to a fully discrete linear finite element approximation with quadrature. It exhibits the phenomenon of supraconvergence, more precisely, for s? [1,2] order O(hs)-convergence of the finite difference solution, and its gradient is shown if the exact solution is in the Sobolev space H1+s(O). In the case of an equation with mixed derivatives in a domain containing oblique boundary sections, the convergence order is reduced to O(h3/2-e) with e > 0 if u? H3(O). The second-order accuracy of the finite difference gradient is in the finite element context nothing else than the supercloseness of the gradient. For s? , the given error estimates are strictly local. | URI: | https://hdl.handle.net/10316/8984 | DOI: | 10.1385/CBB:44:3:539 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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